Yunohost is not really good at being run this way. At least not out of the box.
Two main issues:
DNS records will point to the CNAME of the FritzBox and the reverse lookup is not changeable (obviously). So, Yunohost will always complain about the certificates - despite letscencrypt will happily sign those.
The more tricky problem is sending mails.
A lot of the services rely on being able to send mails. Partially for initial passwords or for other stuff.
The vanilla postfix configuration is rather complex and it’s not easy to figure out how to get going.
What I did, was to relay all mail via a dedicated small server that I have rented somewhere at Netcup and rewrite the mails in a way that my real mail provider would happily eat those.
The Yunohost postfix configuration had to get mangled as well, to play along and not deliver all mails locally, which it otherwise did.
In hindsight I should have documented all the steps that I did, but there was a log of force and back involved and I was too busy to try to get it to work to think about documenting it.